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Generalized Gaussian Process Regression Model for Non-Gaussian Functional Data

Lookup NU author(s): Dr Bo Wang, Dr Jian Shi

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Abstract

In this article, we propose a generalized Gaussian process concurrent regression model for functional data, where the functional response variable has a binomial, Poisson, or other non-Gaussian distribution from an exponential family, while the covariates are mixed functional and scalar variables. The proposed model offers a nonparametric generalized concurrent regression method for functional data with multidimensional covariates, and provides a natural framework on modeling common mean structure and covariance structure simultaneously for repeatedly observed functional data. The mean structure provides overall information about the observations, while the covariance structure can be used to catch up the characteristic of each individual batch. The prior specification of covariance kernel enables us to accommodate a wide class of nonlinear models. The definition of the model, the inference, and the implementation as well as its asymptotic properties are discussed. Several numerical examples with different non-Gaussian response variables are presented. Some technical details and more numerical examples as well as an extension of the model are provided as supplementary materials.

Publication metadata

Author(s): Wang B, Shi JQ

Publication type: Article

Publication status: Published

Journal: Journal of the American Statistical Association

Year: 2014

Volume: 109

Issue: 507

Pages: 1123-1133

Print publication date: 01/01/2014

Acceptance date: 07/03/2014

ISSN (print): 0162-1459

ISSN (electronic): 1537-274X

Publisher: American Statistical Association

URL: http://dx.doi.org/10.1080/01621459.2014.889021

DOI: 10.1080/01621459.2014.889021

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